CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

The question is from CAT Geometry - Triangles. In this problem two sides of a triangle are given and we have to find the third side for the maximum area of the triangle. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems. This problem shows that knowing all the formulae for computing area of a triangle helps.

Question 3: Sides of a triangle are 6, 10 and x for what value of x is the area of the △ the maximum?

1. 8 cms
2. 9 cms
3. 12 cms
4. None of these

Explanatory Answer

Method of solving this CAT Question from Triangles: It helps to know all the formulae for computing area of a triangle. Knowing only Hero's formula can land one in trouble on occasions.

Side of a triangle are. 6, 10, x.
Area = 1/2 * 6 * 10 * sin∠BAC.
Area is maximum, when ∠BAC = 90◦
x = √(100+36) = √136
There is a more algebraic method using hero’s formula. Try that also.

The question is "Sides of a triangle are 6, 10 and x for what value of x is the area of the △ the maximum?"

Hence, the answer is None of these.

Choice D is the correct answer.